Quantum-Secure Covert Communications Over Lossy Bosonic Random Access Channels

Quantum-secure covert communication is an emerging technology crucial for secure transmission in hostile environments. However, existing studies primarily focus on single-transmitter scenarios, leaving a gap in the research on multi-user settings. This paper investigates the fundamental limits of quantum-secure covert communications over lossy bosonic random access channels with Gaussian thermal noise in view of realistic communication systems. The square root law is first established in the scenario where only randomly activated covert users exist. We then demonstrate that the square root law can be surpassed with the assistance of randomly activated overt users in quantum communication system, enabling covert users to transmit O(N) bits of information over N channel uses, provided that the mean photon numbers of all users reaching the detecting end are equal. To prove this, a recursive upper bound is developed on the trace distance (TD) to measure the detection probability of the warden, which is tighter than the traditional quantum relative entropy measurement. However, if the mean photon number of any covert user deviates from the above condition, its covert capacity will degrade to (Formula presented) bits, whereas the capacities of other users will remain at (Formula presented) bits. This result is derived by exploiting the iterative relationship of the upper bound of TD and introducing a two-step detection strategy for the warden to handle random user activation uncertainty. Numerical experiments validate the theoretical findings, confirming the performance of covert transmission in both scenarios.